THE SU(NU) CALOGERO SPIN SYSTEM

A one-dimensional quantum particle system in which particles with su(v ) spins interact through inverse square interactions is introduced. We refer to it as the SU(v) Calogero spin system. Using the quantum inve rse scattering method, we reveal algebraic structures of the system: h idden symmetry is the U(v)similar or equal to SU(v) x U(1) current alg ebra. This is consistent with the fact that the ground-state wave func tion is a solution of the Knizhnik-Zamolodchikov equation. Furthermore we show that the system has a higher symmetry, known as the w(1+infin ity) algebra. With this W-algebra we have a unified viewpoint on the i ntegrable quantum particle systems with long-range interactions such a s the Calogero type (1/x(2)-interactions) and Sutherland type (1/sin(2 ) x-interactions). The Yangian symmetry is briefly discussed.